Move material actions separately in NLA for duplicated objects
You can't create different animations for same material, because NLA-tracks belong to the material, not to the objects. But there is a walkaround, to make that you want:

You can use one material that will be displayed differently depending on the properties of the object. For example, object index:

Object index sets in object properties. Relations tab:

 

Then using node setup, like this, you can set different settings for different object using same material.